It is said that a graph G is independent-set-deletable factor-critical （in short, ID-factor-critical）, if, for everyindependent-set I which has the same parity as ｜V（G）｜, G - I has a perfect matching. A graph G ...It is said that a graph G is independent-set-deletable factor-critical （in short, ID-factor-critical）, if, for everyindependent-set I which has the same parity as ｜V（G）｜, G - I has a perfect matching. A graph G is strongly IM-extendable, if for every spanning supergraph H of G, every induced matching of H is included in a perfect matching of H. The κ-th power of G, denoted by G^κ, is the graph with vertex set V（G） in which two vertices are adjacent if and only if they have distance at most k in G. ID-factor-criticality and IM-extendability of power graphs are discussed in this article. The author shows that, if G is a connected graph, then G^3 and T（G） （the total graph of G） are ID-factor-critical, and G^4 （when ｜V（G）｜ is even） is strongly IM-extendable; if G is 2-connected, then D^2 is ID-factor-critical.展开更多
Ewa·Wojcicka [1] has proved that the connected 3 γ critical graphs has a H path and has put forward to such a conjecture: Connected 3 γ critical graphs without endpoints are H graphs. In this paper,we prove tha...Ewa·Wojcicka [1] has proved that the connected 3 γ critical graphs has a H path and has put forward to such a conjecture: Connected 3 γ critical graphs without endpoints are H graphs. In this paper,we prove that if G is a connected 3 γ critical graph without endpoints and has a H paht ap →a such that d(a,b)=3, then G is a H graph. The result partially solves Ewa. Wojcickas conjecture.展开更多
The main contribution in this article is threefold:(1)we show the necessary and sufficient condition for graphs to be fractional(g,f)-covered which can be expressed in different forms,and extended to fractional(g,f,m)...The main contribution in this article is threefold:(1)we show the necessary and sufficient condition for graphs to be fractional(g,f)-covered which can be expressed in different forms,and extended to fractional(g,f,m)-covered graphs;(2)the concept of fractional-critical covered graph is put forward and its necessary and sufficient condition is given;(3)we present the degree condition for a graph to be fractional(g,f,n′,m)-critical covered,and show that degree bound is sharp when m is small.Moreover,the related result in fractional(a,b,n′,m)-critical covered setting is also verified.展开更多
The utilization of machine learning methods to predict the superconducting critical temperature(T_(c))traditionally necessitates manually constructing elemental features,which challenges both the provision of meaningf...The utilization of machine learning methods to predict the superconducting critical temperature(T_(c))traditionally necessitates manually constructing elemental features,which challenges both the provision of meaningful chemical insights and the accuracy of predictions.In this work,we introduced crystal structure graph neural networks to extract structure-based features for T_(c)prediction.Our results indicated that these structure-based models outperformed all previously reported models,achieving an impressive coefficient of determination(R^(2))of 0.962 and a root mean square error(RMSE)of 6.192 K.From the existing Inorganic Crystal Structure Database(ICSD),our model successfully identified 76 potential high-temperature superconducting compounds with T_(c)≥77 K.Among these,Tl_(5)Ba_(6)Ca_(6)Cu_(9)O_(29)and TlYBa_(2)Cu_(2)O_(7)exhibit remarkably high T_(c)values of 108.4 and 101.8 K,respectively.This work provides a perspective on the structure-property relationship for reliable T_(c)prediction.展开更多
A new static task scheduling algorithm named edge-zeroing based on dynamic critical paths is proposed. The main ideas of the algorithm are as follows: firstly suppose that all of the tasks are in different clusters; s...A new static task scheduling algorithm named edge-zeroing based on dynamic critical paths is proposed. The main ideas of the algorithm are as follows: firstly suppose that all of the tasks are in different clusters; secondly, select one of the critical paths of the partially clustered directed acyclic graph; thirdly, try to zero one of graph communication edges; fourthly, repeat above three processes until all edges are zeroed; finally, check the generated clusters to see if some of them can be further merged without increasing the parallel time. Comparisons of the previous algorithms with edge-zeroing based on dynamic critical paths show that the new algorithm has not only a low complexity but also a desired performance comparable or even better on average to much higher complexity heuristic algorithms.展开更多
The cutwidth of a graph G is the minimum number of overlap edges when G is embedded into a path Pn.The cutwidth problem for a graph G is to determine the cutwidth of G.A graph G with cutwidth k is k-cutwidth critical ...The cutwidth of a graph G is the minimum number of overlap edges when G is embedded into a path Pn.The cutwidth problem for a graph G is to determine the cutwidth of G.A graph G with cutwidth k is k-cutwidth critical if every proper subgraph of G has cutwidth less than k and G is homeomorphically minimal.In this paper,we completely investigated methods of forming a k-cutwidth(k>1)critical tree T.展开更多
The edge-domsaturation number ds'(G) of a graph G = (V, E) is the least positive integer k such that every edge of G lies in an edge dominating set of cardinality k. In this paper, we characterize unicyclic graphs...The edge-domsaturation number ds'(G) of a graph G = (V, E) is the least positive integer k such that every edge of G lies in an edge dominating set of cardinality k. In this paper, we characterize unicyclic graphs G with ds'(G) = q – Δ'(G) + 1 and investigate well-edge dominated graphs. We further define γ'–-critical, γ'+-critical, ds'–-critical, ds'+-critical edges and study some of their properties.展开更多
The development and the revolution of nanotechnology require more and effective methods to accurately estimating the timing analysis for any CMOS transistor level circuit. Many researches attempted to resolve the timi...The development and the revolution of nanotechnology require more and effective methods to accurately estimating the timing analysis for any CMOS transistor level circuit. Many researches attempted to resolve the timing analysis, but the best method found till the moment is the Static Timing Analysis (STA). It is considered the best solution because of its accuracy and fast run time. Transistor level models are mandatory required for the best estimating methods, since these take into consideration all analysis scenarios to overcome problems of multiple-input switching, false paths and high stacks that are found in classic CMOS gates. In this paper, transistor level graph model is proposed to describe the behavior of CMOS circuits under predictive Nanotechnology SPICE parameters. This model represents the transistor in the CMOS circuit as nodes in the graph regardless of its positions in the gates to accurately estimating the timing analysis rather than inaccurate estimating which caused by the false paths at the gate level. Accurate static timing analysis is estimated using the model proposed in this paper. Building on the proposed model and the graph theory concepts, new algorithms are proposed and simulated to compute transistor timing analysis using RC model. Simulation results show the validity of the proposed graph model and its algorithms by using predictive Nano-Technology SPICE parameters for the tested technology. An important and effective extension has been achieved in this paper for a one that was published in international conference.展开更多
基金Project supported by NSFC(10371112)NSFHN (0411011200)SRF for ROCS,SEM
文摘It is said that a graph G is independent-set-deletable factor-critical （in short, ID-factor-critical）, if, for everyindependent-set I which has the same parity as ｜V（G）｜, G - I has a perfect matching. A graph G is strongly IM-extendable, if for every spanning supergraph H of G, every induced matching of H is included in a perfect matching of H. The κ-th power of G, denoted by G^κ, is the graph with vertex set V（G） in which two vertices are adjacent if and only if they have distance at most k in G. ID-factor-criticality and IM-extendability of power graphs are discussed in this article. The author shows that, if G is a connected graph, then G^3 and T（G） （the total graph of G） are ID-factor-critical, and G^4 （when ｜V（G）｜ is even） is strongly IM-extendable; if G is 2-connected, then D^2 is ID-factor-critical.
文摘Ewa·Wojcicka [1] has proved that the connected 3 γ critical graphs has a H path and has put forward to such a conjecture: Connected 3 γ critical graphs without endpoints are H graphs. In this paper,we prove that if G is a connected 3 γ critical graph without endpoints and has a H paht ap →a such that d(a,b)=3, then G is a H graph. The result partially solves Ewa. Wojcickas conjecture.
基金the National Natural Science Foundation of China(Nos.12161 and 12031018).
文摘The main contribution in this article is threefold:(1)we show the necessary and sufficient condition for graphs to be fractional(g,f)-covered which can be expressed in different forms,and extended to fractional(g,f,m)-covered graphs;(2)the concept of fractional-critical covered graph is put forward and its necessary and sufficient condition is given;(3)we present the degree condition for a graph to be fractional(g,f,n′,m)-critical covered,and show that degree bound is sharp when m is small.Moreover,the related result in fractional(a,b,n′,m)-critical covered setting is also verified.
基金supported by Guangdong Basic and Applied Basic Research Foundation(2022A1515110676 and2024A1515011845)Shenzhen Science and Technology Program(JCYJ20220531095404009,RCBS20221008093057027,and JCYJ20230807094313028)the Project Supported by Sunrise(Xiamen)Photovoltaic Industry Co.,Ltd.(Development of Artificial Intelligence Technology for Perovskite Photovoltaic Materials,HX20230176)。
文摘The utilization of machine learning methods to predict the superconducting critical temperature(T_(c))traditionally necessitates manually constructing elemental features,which challenges both the provision of meaningful chemical insights and the accuracy of predictions.In this work,we introduced crystal structure graph neural networks to extract structure-based features for T_(c)prediction.Our results indicated that these structure-based models outperformed all previously reported models,achieving an impressive coefficient of determination(R^(2))of 0.962 and a root mean square error(RMSE)of 6.192 K.From the existing Inorganic Crystal Structure Database(ICSD),our model successfully identified 76 potential high-temperature superconducting compounds with T_(c)≥77 K.Among these,Tl_(5)Ba_(6)Ca_(6)Cu_(9)O_(29)and TlYBa_(2)Cu_(2)O_(7)exhibit remarkably high T_(c)values of 108.4 and 101.8 K,respectively.This work provides a perspective on the structure-property relationship for reliable T_(c)prediction.
文摘A new static task scheduling algorithm named edge-zeroing based on dynamic critical paths is proposed. The main ideas of the algorithm are as follows: firstly suppose that all of the tasks are in different clusters; secondly, select one of the critical paths of the partially clustered directed acyclic graph; thirdly, try to zero one of graph communication edges; fourthly, repeat above three processes until all edges are zeroed; finally, check the generated clusters to see if some of them can be further merged without increasing the parallel time. Comparisons of the previous algorithms with edge-zeroing based on dynamic critical paths show that the new algorithm has not only a low complexity but also a desired performance comparable or even better on average to much higher complexity heuristic algorithms.
基金Supported by Soft Science Foundation of Henan Province(Grant No.192400410212)the Science and Technology Key Project of Henan Province of China(Grant No.22210211008)。
文摘The cutwidth of a graph G is the minimum number of overlap edges when G is embedded into a path Pn.The cutwidth problem for a graph G is to determine the cutwidth of G.A graph G with cutwidth k is k-cutwidth critical if every proper subgraph of G has cutwidth less than k and G is homeomorphically minimal.In this paper,we completely investigated methods of forming a k-cutwidth(k>1)critical tree T.
文摘The edge-domsaturation number ds'(G) of a graph G = (V, E) is the least positive integer k such that every edge of G lies in an edge dominating set of cardinality k. In this paper, we characterize unicyclic graphs G with ds'(G) = q – Δ'(G) + 1 and investigate well-edge dominated graphs. We further define γ'–-critical, γ'+-critical, ds'–-critical, ds'+-critical edges and study some of their properties.
文摘The development and the revolution of nanotechnology require more and effective methods to accurately estimating the timing analysis for any CMOS transistor level circuit. Many researches attempted to resolve the timing analysis, but the best method found till the moment is the Static Timing Analysis (STA). It is considered the best solution because of its accuracy and fast run time. Transistor level models are mandatory required for the best estimating methods, since these take into consideration all analysis scenarios to overcome problems of multiple-input switching, false paths and high stacks that are found in classic CMOS gates. In this paper, transistor level graph model is proposed to describe the behavior of CMOS circuits under predictive Nanotechnology SPICE parameters. This model represents the transistor in the CMOS circuit as nodes in the graph regardless of its positions in the gates to accurately estimating the timing analysis rather than inaccurate estimating which caused by the false paths at the gate level. Accurate static timing analysis is estimated using the model proposed in this paper. Building on the proposed model and the graph theory concepts, new algorithms are proposed and simulated to compute transistor timing analysis using RC model. Simulation results show the validity of the proposed graph model and its algorithms by using predictive Nano-Technology SPICE parameters for the tested technology. An important and effective extension has been achieved in this paper for a one that was published in international conference.
